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nydus/The First Steps in AlgebraPublic

This textbook introduces the fundamental concepts of algebra, including definitions of units, quantities, and number symbols. It explains the use of letters to represent numbers and outlines the signs for basic mathematical operations.

Page 93 of 227

Table of Contents

VIII.

Find the product of all the different factors, taking each factor the greatest number of times it occurs in any of the given expressions.

Exercise 41.

Find the L. C. M. of:

$9 x y^{3}$ and $6 x^{2} y$ .

$3 a b c^{2}$ and $2 a^{2} b c^{3}$ .

$4 a^{3} b$ and $10 a b^{3}$ .

$6 a^{3} b^{3}$ and $15 a^{2} b^{4}$ .

$21 x y^{3}$ and $27 x^{3} y^{5}$ .

$x y^{3} z^{2}$ and $x^{2} y^{2} z^{3}$ .

$a^{2}$ and $a^{2} + a$ .

$x^{2}$ and $x^{3} - 3 x^{2}$ .

$x^{2} - 1$ and $x^{2} + x$ .

$x^{2} - 1$ and $x^{2} - x$ .

$x^{2} + x y$ and $x y + y^{2}$ .

$x^{2} + 2 x$ and $(x + 2)^{2}$ .

$a^{2} + 4 a + 4$ and $a^{2} + 5 a + 6$ .

$c^{2} + c - 20$ and $c^{2} - c - 30$ .

$b^{2} + b - 42$ and $b^{2} - 11 b + 30$ .

$y^{2} - 10 y + 24$ and $y^{2} + y - 20$ .

$z^{2} + 2 z - 35$ and $z^{2} - 11 z + 30$ .

$x^{2} - 64; x^{3} - 64$ ; and $x + 8$ .

$a^{2} - b^{2}; (a + b)^{2}$ ; and $(a - b)^{2}$ .

$4 a b (a + b)^{2}$ and $2 a^{2} (a^{2} - b^{2})$ .

$y^{2} + 7 y + 12; y^{2} + 6 y + 8$ ; and $y^{2} + 5 y + 6$ .

$x^{2} - 1; x^{3} + x^{2} + x + 1$ ; and $x^{3} - x^{2} + x - 1$ .

$1 - x^{2}; 1 - x^{3}$ ; and $1 + x$ .

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